Curve reconstruction from noisy samples
The method of Lee [1]} uses a neighborhood graph, the Euclidean Minimum Spanning Tree, to connect noisy samples.
It then smoothens this thick graph using a variant of Moving Least Squares [2]} and applies a spline fit.
Their method is limited to single open curves and does not handle varying sample density or noises well.
Screened Poisson [3]} relies on given normals for noisy point cloud reconstruction [4]}, however normals from sensor input are often noisy as well.
Robust HPR [5]} extracts connectivity locally from a transformation of the convex hull and combines it in a weighted global graph.
However, it often exhibits gaps in the reconstruction and does not produce a denoised curve.
 [6]} solve a related problem and can also reconstruct intersecting curves by greedily simplifying a Delaunay triangulation of the point set but fail to connect curves with non-uniform sampling or noise.
A related method [7]} also fails for non-uniform sampling.
One method [8]} moves and eliminates balls centered on samples to obtain a sparse piece-wise linear fit but shows results only on simple cases with very dense sampling.
The recent method FitConnect [9]} fits circular neighborhoods, as has been shown to work well [10]}, and determine the inside/outside of the curve locally.
FitConnect increases the neighborhood size for the fits until they become consistent with each other, eliminating samples in the process that do not contribute to the connectivity.
They guarantee manifold construction for arbitrarily high noise, provided that the features emerge over the noise extent, and provide an estimate of the local noise at samples.
This algorithm is a direct extension of a reconstruction algorithm handling noise-free samples under very relaxed conditions [11]}, which also gives a detailed overview of prior such work as important groundwork in this field.
As a post-processing, FitConnect blends the locally determined neighborhood fits along normals, but this can result in jagged edges where fits vary much in size, or where it interpolates samples where the noise extent is too low to be detected.
We will use the connectivity reconstruction algorithm of FitConnect [9]} and apply a denoising algorithm based on the properties recovered together with that connectivity. As a result, we are able to both denoise interpolated points with a specified noise extent and avoiding jagged edges.
